critique of the kalam cosmological argument extracted pages from philosophy_of_religion

objects do not stand in causal relations. Therefore,the transcendent cause of the origin of the universemust be of the order of mind. Third, this sameconclusion is also implied by the fact that we havein this case the origin of a temporal effect from atimeless cause. If the cause of the origin of the uni-verse were an impersonal set of necessary and suffi-cient conditions, it would be impossible for thecause to exist without its effect. For if the necessaryand sufficient conditions of the effect are timelessly

given, then their effect must be given as well. Theonly way for the cause to be timeless and changelessbut for its effect to originate anew a finite time agois for the cause to be a personal agent who freelychooses to bring about an effect without antecedentdetermining conditions. Thus we are brought, notmerely to a transcendent cause of the universe, butto its Personal Creator. He is, as Leibniz main-tained, the Sufficient Reason why anything existsrather than nothing.

NOTES

1. This should not be taken to mean that the densityof the universe takes on a value of H0 but ratherthat the density of the universe is expressed by aratio of mass to volume in which the volume iszero; since division by zero is impermissible, thedensity is said to be infinite in this sense.

2. Quentin Smith, “The Uncaused Beginning of theUniverse,” in Theism, Atheism and Big BangCosmology, by William Lane Craig and QuentinSmith (Oxford: Clarendon, 1993), p. 120.

3. Arthur Eddington, The Expanding Universe(New York: Macmillan, 1933), p. 124.

4. Ibid., p. 178.

5. Stephen Hawking and Roger Penrose, The Natureof Space and Time, The Isaac Newton InstituteSeries of Lectures (Princeton, N.J.: PrincetonUniversity Press, 1996), p. 20.

6. Richard Schlegel, “Time and Thermodynamics,”in The Voices of Time, ed. J. T. Fraser (London:Penguin, 1948), p. 511.

II.B.5

A Critique of the Kalam Cosmological ArgumentPAUL DRAPER

Paul Draper is professor of philosophy at Purdue University and the author of several important essays inthe philosophy of religion. In this article he analyzes William Lane Craig’s philosophical defense of thekalam cosmological argument. Draper contends that Craig’s defense fails, both because it fails to establishthat the universe had a beginning and because it rests on an equivocation of the phrase ‘begins to exist.’

Copyright © Paul Draper 1997. Used by permission of the author.

172 PART II • TRAD IT IONAL ARGUMENTS FOR THE EX I STENCE OF GOD

Epistemology begins in doubt, ethics in conflict, andmetaphysics in wonder.

In a recent book,1 William Lane Craig offers a phil-osophical and scientific defense of a very old andvery wonderful argument: the kalam cosmologicalargument. Unlike other cosmological arguments,the kalam argument bases its conclusion that theuniverse has a cause of its existence on the premisethat the universe began to exist a finite time ago.Craig calls it the “kalam” cosmological argumentbecause “kalam” is the name of a theological move-ment within Islam that used reason, including thisargument, to defend the Muslim faith against phil-osophical objections. After being fully developed byArab thinkers like al-Kindi and al-Ghazali, theargument eventually made its way to the West,where it was rejected by St. Thomas Aquinas anddefended by St. Bonaventure.2 My focus in thispaper will be on Craig’s philosophical defense ofthe argument. I will try to show that this defensefails, both because it fails to establish that the uni-verse had a beginning and because it commits thefallacy of equivocation.

Compare the following two cosmologicalarguments, each of which concludes that the uni-verse has a cause of its existence:

1. Every contingent thing (including things thatare infinitely old) has a cause of its existence.

2. The universe is contingent.

3. Therefore, the universe has a cause of itsexistence.

1. Everything that begins to exist has a cause of itsexistence.

2. The universe began to exist.

3. Therefore, the universe has a cause of itsexistence.

The first of these arguments is sometimes called theargument from contingency. It was suggested byAristotle, clearly formulated by Arabic philoso-phers like ibn Sina, and later championed in theWest by St. Thomas Aquinas. I find it completelyunpersuasive. For although the second premise isclearly true (so long as “contingent” means “logically

contingent”), I do not find the first premise appeal-ing at all. If something is infinitely old, then it hasalways existed, and it’s hard to see why somethingthat has always existed requires a cause of its exis-tence, even if it is logically possible that it not haveexisted. (Indeed, it’s not even clear that somethingthat has always existed could have a cause of itsexistence.)

The second of these arguments is the kalamcosmological argument. This argument avoidsthe weakness of the argument from contingency bydenying that the universe is infinitely old and main-taining that the universe needs a cause, not because itis contingent, but rather because it had a beginning.In other words, it replaces the weak premise thatevery contingent thing needs a cause of its existencewith the compelling premise that everything thatbegins to exist needs a cause of its existence. Ofcourse, a price must be paid for strengthening thefirst premise: the second premise—that the universebegan to exist—is not by a long shot as unquestion-ably true as the claim that the universe is contingent.

Craig, however, provides a spirited and plausi-ble defense of this premise. He offers fourarguments in support of it, two of which are phil-osophical (armchair cosmology at its best) and twoof which are scientific (but still interesting). Bothphilosophical arguments depend on a distinctionbetween a potential infinite and an actual infinite.A potential infinite is a series or collection that canincrease forever without limit but is always finite(e.g., the set of events that have occurred sincethe birth of my daughter or the set of completedyears after 1000 BCE). An actual infinite is a setof distinct things (real or not) whose number isactually infinite (e.g., the set of natural numbers).The first philosophical argument claims that therecan’t be an infinite regress of events, because actualinfinites cannot exist in reality. According to thesecond argument, an infinite regress of events isimpossible because, even if actual infinites couldexist in reality, they could not be formed by suc-cessive addition.

The first scientific argument is based on the evi-dence for the Big Bang theory, which seems to manyscientists to support the view that the universe had a

PAUL DRAPER • A CR IT IQUE OF THE KAL AM COSMOLOG ICAL ARGUMENT 173

beginning. The second scientific argument appealsto the Second Law of Thermodynamics. Accordingto this law, the amount of energy available to domechanical work always decreases in a closed system.Thus, since the universe as a whole is a closed systemwith a finite amount of such energy, an infinitely olduniverse is incompatible with the fact that we havenot yet run out of such energy—the universe has notyet reached its “equilibrium end state.” Since I’m noscientist, I will focus my attention on Craig’s philo-sophical arguments, beginning with the second one.

As Craig himself points out, his second philo-sophical argument is very similar to the argumentthat Immanuel Kant uses to support the thesis of hisfirst antinomy:

If we assume that the world has nobeginning in time, then up to every givenmoment an eternity has elapsed and therehas passed away in the world an infiniteseries of successive states of things. Nowthe infinity of a series consists in the factthat it can never be completed throughsuccessive synthesis. It thus follows that it isimpossible for an infinite world-series tohave passed away, and that a beginningof the world is therefore a necessarycondition of the world’s existence.3

Craig formulates the argument as follows:

(i) The temporal series of events is a collectionformed by successive addition.

(ii) A collection formed by successive additioncannot be an actual infinite.

(iii) Thus, the temporal series of events cannot bean actual infinite. (from i and ii)

(iv) Therefore, the temporal regress of events isfinite. (from iii)4

This argument is closely related to Zeno’s paradoxes,which depend on the claim that one cannot com-plete an infinite series of tasks one at a time since thatwould imply an infinitieth member of the series. Asit stands, the argument is unconvincing. For while itis true that one cannot start with a finite collectionand then by adding one new member at a time turnit into an infinite collection (no matter how much

time one has available), nothing of the sort isrequired in order for the past to be infinite. For ifthe temporal regress of events is infinite, then theuniverse has never had a finite number of past events.Rather, it has always been the case that the collec-tion of past events is infinite. Thus, if the temporalregress of events is infinite, then the temporal seriesof events is not an infinite collection formed by suc-cessively adding to a finite collection. Rather, it is acollection formed by successively adding to an infi-nite collection. And surely it is not impossible toform an infinite collection by successively adding toan already infinite collection.

One might object that, if the temporal regressof events is infinite, then there must be some eventE separated from the birth of my daughter by aninfinite number of intermediate events, in whichcase the collection containing E and all those inter-mediate events would have to be an actually infinitecollection formed by successively adding to a finitecollection of events, namely the collection contain-ing E as its only member. This objection failsbecause it is simply not true that, if the temporalregress of events is infinite, then there must be twoevents separated by an infinite number of interme-diate events. For consider the set of natural num-bers. It is actually infinite, yet every member of it issuch that there is a finite number of membersbetween it and its first member.5

Craig’s first philosophical argument is, I believe,much more promising than his second. It bases itsconclusion that the temporal regress of physicalevents must be finite—there must have been a firstphysical event—on the premises that an actual infinitecannot exist in reality and an infinite temporal regressof events is an actual infinite.6 From this and the fur-ther claim that a first physical event could not havebeen preceded by an eternal absolutely quiescentphysical universe, the conclusion is drawn that thephysical universe had a beginning. The first stage ofthis argument can be formulated as follows:

a. No set of real things is actually infinite.

b. If there was no first event, then the set of allreal events occurring prior to the birth of mydaughter is actually infinite.

c. Therefore, there was a first event.


Craig defends premise (a) of this argumentby pointing out that the assumption that a set ofreal things is actually infinite has paradoxical implica-tions.7 For example, it implies that we could have alibrary consisting of infinitely many black books(each might be assigned an even number). Wecould then add infinitely many red books (eachmight be assigned an odd number) and yet notincrease the number of books in the library by asingle volume. Indeed, we could add infinitelymany different colors of books with infinitely manybooks of each color (the red books could be assignedrational numbers between 0 and 1, the black booksrational numbers between 1 and 2, and so on) andnot increase our collection by a single volume.

These paradoxes arise because the followingthree statements constitute an inconsistent triad:

S1. A set has more members than any of its propersubsets.

S2. If the members of two sets can be placed inone-to-one correspondence, then neither sethas more members than the other.

S3. There are actually infinite sets.

For example, since the set of even numbers hasone-to-one correspondence with the set of naturalnumbers and even with the set of rational numbers,S2 implies that one could add infinitely manyred books or infinitely many books of each ofinfinitely many different colors to the library with-out increasing the size of that library’s collection.(One need only make sure that the additions aredenumerably infinite.) But of course S1 implies thatany such addition would increase the size of thecollection since the set of even numbers is a propersubset both of the set of natural numbers and ofthe set of rational numbers. Thus, two intuitivelyappealing principles together imply a contradictionon the assumption that there can be an actuallyinfinite collection of books. One way to avoidthis contradiction is to reject the assumption thatthere can be an actually infinite collection ofbooks. So the underlying argument in defense ofthe claim that no collection of real things is actuallyinfinite is simply that, since S1 and S2 are both trueof collections of real things, it follows that S3 is not

true of such collections—no collections of realthings are actually infinite.

Craig claims that Georg Cantor’s theory oftransfinite numbers is consistent because it rejectsthe first member of the triad. But this member isnot rejected because it can be proven false aboutactually infinite sets, nor is the second memberaccepted because it can be proven that if a one-to-one correspondence between the elements oftwo actually infinite sets can be established thenthe sets are equivalent. Rather, equivalent sets aresimply defined as sets having one-to-onecorrespondence. Thus, while Cantor’s theory is aconsistent mathematical system, there is, accordingto Craig, no reason to think that it has any interest-ing ontological implications. In particular, it doesnot provide any reason to think that S1 is falseabout actually infinite sets and hence provides nojustification for thinking that actual infinites canexist in reality.8

Notice that, if Craig is right that past events arereal but future events are not, then his argument fora first event does not commit him to the positionthat there is a last event. For consider the followingparallel argument for the conclusion that there willbe a last event:

(a) No set of real things is actually infinite.

(b) If there will be no last event, then the set of allreal events occurring after the birth of mydaughter is actually infinite.

(c) Therefore, there will be a last event.

Since future events are not real, the second premiseof this argument is false. If there is no last event,then the set of all real events occurring afterthe birth of my daughter is merely potentiallyinfinite—not actually infinite. This collection canincrease in size indefinitely, but it will always befinite. Past events, on the other hand, are all real.So if there is no first past event, then the set of allreal past events is actually infinite, not potentiallyinfinite. Craig concludes that, although there maybe no last event, there must be a first event, andhence, since matter cannot exist without eventsoccurring, it follows that the universe has notalways existed—it began to exist.


Although this fascinating argument for the sec-ond premise of the kalam argument may be sound,Craig has not given us adequate reason to believe itis. The problem concerns the inconsistent triadmentioned above. What Craig needs to do is toshow that, when it comes to collections of realthings, we should reject the third member of thetriad instead of S1 or S2. But he has not shown this.S1 and S2 are certainly true for finite collections.But it’s far from clear that they are true for all col-lections. Allow me to explain why.

Consider S1, which says that a set has moremembers than any of its proper subsets. If “more”means “a greater number,” then the claim that S1 istrue for actually infinite sets requires us to makesense of claiming that actually infinite sets have anumber of members. But an actually infinite setdoesn’t have a natural number of members or arational number of members or a real number ofmembers, so one such set can’t have a greater natu-ral or rational or real number of members thananother. Of course, an actually infinite set doeshave a transfinite number of members. But transfi-nite numbers are what Cantor defines them to be.And given his definition, it simply isn’t true thatactually infinite sets have a greater transfinite num-ber of members than all of their proper subsets. Wecould say that an actually infinite set has a greater“infinite number” of members than all of its propersubsets, but Craig gives us no theory of infinitenumbers that would justify that claim.

Of course, Craig might claim that no such theoryis necessary, that we don’t even need to make use ofthe word number here; for it’s just obvious that, insome sense of the word more, any set that has everymember that another set has and some members itdoesn’t have has more members than the other set. Iagree this is obvious, but in the case of infinite sets, thisis obvious only because “more” can just mean “hasevery member the other set has and some members itdoesn’t have.” If, however, we grant Craig that S1 istrue on these grounds, then why accept S2? Why notclaim instead that actually infinite collections of realobjects are possible, but the fact that two of them haveone-to-one correspondence is not a good reason tobelieve that neither has “more” members than theother? Why, for example, is it more reasonable to

believe that actually infinite libraries are impossiblethan to believe that, although they are possible, onesuch library can have “more” books than a seconddespite the fact that the books in the first can be placedin one-to-one correspondence with the books in thesecond? Craig provides no good answer to these ques-tions. Obviously he cannot all of a sudden appeal toCantor’s theory to justify accepting S2. For thatwould commit him to rejecting S1. And since,when infinite sets are compared, the word more can-not mean what it does when finite sets are compared,the fact that S2 is true for finite sets is not by itself agood reason to believe that it is true for all sets.

So Craig fails to show that S1 and S2 are bothtrue of all collections of real objects, and hence hefails to show that actually infinite collections of realobjects are impossible. Therefore, his first philo-sophical argument, like his second, fails to establishthat an infinite regress of events is impossible and sofails to establish that the universe began to exist.This leaves us with Craig’s scientific arguments.Since I lack the expertise to evaluate these argu-ments, let’s assume, for the sake of argument, thatthey succeed and hence that the universe did beginto exist. Must we then conclude that the kalamargument succeeds? This would be a profoundresult. Granted, this argument doesn’t get all theway to God’s existence. But accepting its conclu-sion does require rejecting naturalism—since noth-ing can be a cause of its own existence, a causeoutside the natural world would be required.

As wonderful as this conclusion is, I do notbelieve that Craig’s defense of the kalam argumentjustifies accepting it, even assuming that his scientificarguments are sound. This is because Craig commitsthe fallacy of equivocation. The verb “to begin” has anarrow or strict sense and a broad or loose sense. Inthe narrow sense, “to begin” means “to begin withintime.” When used in this way, “x begins to exist”implies that there was a time at which x did notexist and then a later time at which x exists. But “tobegin” can also mean “to begin either within or withtime.” When used in this way, “x begins to exist”does not imply that there was a time at which x didnot exist, because the past may itself be finite in whichcase something that begins to exist at the first momentin time is such that there never was a time at which it


did not exist—it begins with time rather than withintime. Now consider the two premises of the kalamargument in the fight of this distinction.

The second premise is that the universe began toexist. All of Craig’s arguments in favor of this premise,including his scientific ones, would be unsound if oneinterpreted “began to exist” in the second premise asmeaning “began to exist within time.” For nothing inthese arguments counts against a relational view oftime. And on a relational view of time, a first tempo-ral event is simultaneous with a first moment in time.This would mean that, if the temporal series of pastevents is finite, then the universe began to exist withtime. Indeed, if anything, the arguments in favor ofthe second premise support a beginning with time.For if an infinite regress of events is an actual infiniteand for that reason impossible, then it would seemthat an infinite past would be an actual infinite andfor that reason impossible. Moreover, one of Craig’sscientific arguments appeals to an interpretation of theBig Bang Theory according to which time did notexist “before” the big bang. So the most that Craighas established is that the universe began to existeither within or with time.

The first premise is that anything that begins toexist has a cause of its existence. What does “beginsto exist” mean here? Craig defends this premise byclaiming that it is an “empirical generalisation enjoy-ing the strongest support experience affords.”9 Butexperience only supports the claim that anything thatbegins to exist within time has a cause of its exis-tence. For we have no experience whatsoever ofthings beginning to exist with time.10 Such thingswould require timeless causes. And even if it is con-ceptually possible for a temporal event to have a

timeless cause, we certainly have no experience ofthis. Of course, Craig also claims that premise (1) isintuitively obvious—that it needs no defense at all.But it is far from obvious that a universe that beginsto exist with time needs a cause of its existence. Likean infinitely old universe, a universe that begins toexist with time has always existed—for any time t,the universe existed at t. And once again, it’s far fromobvious that something that has always existedrequires a cause for its existence. It’s not even clearthat such a thing could have a cause of its existence.

So in order to be justified in believing both ofthe premises of the argument—justified, that is,solely on the basis of Craig’s defense of thosepremises—we would need to equivocate on themeaning of “begins to exist.” We would need touse this term in the narrow sense in the first premiseand in the broad sense in the second premise. Butthen the conclusion of the argument would notfollow from its premises. Thus, Craig commits thefallacy of equivocation.11

Do my objections to Craig’s defense of the kalamargument prove that it is doomed? I don’t think so.The argument remains promising. Perhaps, for exam-ple, it could be shown that an absolute theory of timeis correct, and that such a theory, together with sci-entific or new philosophical evidence against an infi-nitely old universe, implies a beginning of theuniverse within time. Or perhaps it could be shownthat the universe began to exist with time and thateven something that begins to exist with timerequires a cause of its existence. So my conclusion isnot that the kalam argument should be dismissed. It isjust that it has not yet been adequately defended. Istill wonder whether the argument is a good one.

NOTES

1. William Lane Craig, The Kalam CosmologicalArgument (New York: Harper & Row Publishers),1979.

2. For a brief but interesting history of the argument,see Craig, Part I.

3. Immanuel Kant, Critique of Pure Reason, trans.Norman Kemp Smith (London: Macmillan & Co.,1929), p. 396. Quoted by Craig on p. 189.

4. Craig, p. 103.

5. Cf. Quentin Smith, “Infinity and the Past,” inTheism, Atheism, and Big Bang Cosmology, ed.William Lane Craig and Quentin Smith (Oxford:Clarendon Press, 1993), pp. 78–83; Antony Flew,“The Case for God Challenged,” in Does GodExist?: The Great Debate, ed. J. P. Moreland and KaiNielsen (Nashville: Thomas Nelson Publishers,


1990), p. 164; and Keith Parsons, “Is There a Casefor Christian Theism?” in Does God Exist?: TheGreat Debate, p. 187.

6. Craig, p. 69.

7. Craig, pp. 82–87.

8. Craig, pp. 94–95.

9. Craig, p. 145. Craig also suggests here that premise(1) could be defended by appealing to an a prioricategory of causality. Such Kantian maneuveringdoes not seem very promising in this context. Forin order to reconcile it with the realism pre-supposed by the kal -am argument, one would needto claim that the causal principle must, as anecessary precondition of thought, hold withoutexception in the noumenal world!

10. Cf. Quentin Smith, “The Uncaused Beginning ofthe Universe,” in Theism, Atheism, and Big BangCosmology, p. 123.

11. In “The Caused Beginning of the Universe” (inTheism, Atheism, and Big Bang Cosmology) Craigdenies that his inference is equivocal on the

grounds that “our conviction of the truth of thecausal principle is not based upon an inductivesurvey of existents in space-time, but rather uponthe metaphysical intuition that something cannotcome out of nothing” (p. 147). Of course, he didappeal to such a survey in his book, but Craigclaims that this was just “a last-ditch defence of theprinciple designed to appeal to the hard-headedempiricist who resists the metaphysical intuitionthat properly grounds our conviction of theprinciple” (p. 147, note 13). This response to thecharge of equivocation is not at all convincing. Formetaphysical intuitions about contingent mattersare notoriously unreliable—that’s why so manycontemporary philosophers are, quite justifiably,“hard-headed empiricists.” Further, at the risk ofcommitting the genetic fallacy, it is worth pointingout that it is probably our experience of thingsbeginning to exist within time that causes some ofus to have the metaphysical intuition that some-thing cannot come out of nothing.

II.C THE TELEOLOGICAL ARGUMENT FORTHE EXISTENCE OF GOD

THE TELEOLOGICAL ARGUMENT for the existence of God begins withthe premise that the world exhibits intelligent purpose, order, or other marks ofdesign, and it proceeds to the conclusion that there must be or probably is a divineintelligence, a supreme designer, to account for the observed or perceived intelli-gent purpose or order. Although core ideas of the argument can be found inPlato, in the Bible (Rom. 1), and in Cicero, the most well-known treatment ofit is found in William Paley’s Natural Theology (1802). In his opening chapter,included here as our first selection, he offers his famous “watch” argument, whichbegins as follows:

In crossing a heath, suppose I pitched my foot against a stone, and wereasked how the stone came to be there, I might possibly answer, that foranything I knew to the contrary, it had lain there for ever; nor would it,perhaps, be very easy to show the absurdity of this answer. But suppose Ifound a watch upon the ground, and it should be inquired how the watchhappened to be in that place, I should hardly think of the answer which Ihad before given—that, for anything I knew, the watch might have alwaysbeen there. Yet why should not this answer serve for the watch as well asfor the stone? Why is it not as admissible in the second case, as in the first?


critique of the kalam cosmological argument extracted pages from philosophy_of_religion

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